Method and system for three-dimensional fabrication

ABSTRACT

A method of three-dimensional fabrication of an object is disclosed. The method comprises: forming a plurality of layers in a configured pattern corresponding to the shape of the three-dimensional object, at least one layer of the plurality of layers being formed at a predetermined and different thickness selected so as to compensate for post-formation shrinkage of the layer along a vertical direction. In various exemplary embodiments of the invention spread of building material of one or more layers is diluted at least locally such as to maintain a predetermined thickness and a predetermined planar resolution for the layer.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/227,049 filed on Aug. 3, 2016, which is a continuation of U.S. patentapplication Ser. No. 14/329,953 filed on Jul. 13, 2014, now U.S. Pat.No. 9,417,627, which is a division of U.S. patent application Ser. No.12/593,970 filed on Sep. 30, 2009, now U.S. Pat. No. 8,784,723, which isa National Phase of PCT Patent Application No. PCT/IL2007/000429 havingInternational Filing Date of Apr. 1, 2007. The contents of the aboveapplications are all incorporated herein by reference.

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to three-dimensional fabrication and, moreparticularly, to a method and system for three-dimensional fabricationof objects having enhanced dimensional accuracy.

Three dimensional fabrication processes are defined as processes inwhich objects are constructed in layers utilizing a computer model ofthe objects. The layers are deposited or formed by a suitable devicewhich receives signals from a computer using, e.g., a computer aideddesign (CAD) software.

Three-dimensional fabrication is typically used in design-related fieldswhere it is used for visualization, demonstration and mechanicalprototyping. Thus, three-dimensional fabrication facilitates rapidfabrication of functioning prototypes with minimal investment in toolingand labor. Such rapid prototyping shortens the product development cycleand improves the design process by providing rapid and effectivefeedback to the designer. Three-dimensional fabrication can also be usedfor rapid fabrication of non-functional parts, e.g., for the purpose ofassessing various aspects of a design such as aesthetics, fit, assemblyand the like. Additionally, three-dimensional fabrication techniqueshave been proven to be useful in the fields of medicine, where expectedoutcomes are modeled prior to performing procedures. It is recognizedthat many other areas can benefit from rapid prototyping technology,including, without limitation, the fields of architecture, dentistry andplastic surgery where the visualization of a particular design and/orfunction is useful.

In the past several years, there has been considerable interest indeveloping computerized three-dimensional fabrication techniques.

One such technique is disclosed, e.g., in U.S. Pat. Nos. 6,259,962,6,569,373, 6,658,314, 6,850,334, 6,863,859 and 7,183,335, U.S. PatentApplication Publication Nos. 20050104241 and 20050069784, and PCT Publ.No. WO/2004/096527, the contents of which are hereby incorporated byreference. In this technique, an interface material is dispensed from aprinting head having a set of nozzles to deposit layers on a supportingstructure. Depending on the interface material, the layers are thencured using a suitable curing device. The interface material may includebuild material, which forms the object, and support material, whichsupports the object as it is being built.

In another such technique, disclosed, e.g., in U.S. Pat. No. 5,204,055,a component is produced by spreading powder in a layer and thendepositing a binder material at specific regions of a layer asdetermined by the computer model of the component. The binder materialbinds the powder both within the layer and between adjacent layers. In amodification of this approach, the powder is raster-scanned with ahigh-power laser beam which fuses the powder material together. Areasnot hit by the laser beam remain loose and fall from the part upon itsremoval from the system.

U.S. Pat. No. 6,193,923 to Leyden et al. discloses a selectivedeposition modeling system which includes a dispensing platformslideably coupled to an X-stage. A multi orifice inkjet head is locatedon the dispensing platform and configured for jetting hot melt inks ontoa part-building platform. The dispensing platform moves back and forthin the X-direction relative to a part-building platform, such that theinkjet head scans the part-building platform while jetting the inksthereon. The head is computer controlled so as to selectively activateits orifices and cause them to simultaneously emit droplets of ink in aconfigured pattern corresponding to the shape of the object.

Leyden et al. contemplate several building styles, including dispensinghigher drop density in down-facing surfaces, up-facing surfaces orboundary regions of the object compared to interior regions of theobject; and building down-facing and up-facing skin regions whichrespectively extend several layers near down-facing and up-facingsurfaces.

Another reference of interest is U.S. Patent Application Publication No.20040159978 to Nielsen et al., which discloses a technique for reducingthe effects of “terracing” in a three dimensional fabrication processes.The terracing effect leaves noticeable visual traces, typically inobjects that have vertically contoured surfaces which spread acrossmultiple layers. To overcome this effect Nielsen et al. vary the amountof binder or build material added across each layer, such that thethickness of the layer is gradually decreased in transition regionsbetween successive terraced layers.

Also of interest is a three-dimensional fabrication technique known asstereolithography, disclosed, e.g., in U.S. Pat. No. 4,575,330. In thistechnique, a focused ultra-violet (UV) laser scans the top of a bath ofa photopolymerizable liquid material. The UV laser causes the bath topolymerize where the laser beam strikes the surface of the bath,resulting in the creation of a solid plastic layer just below thesurface. The solid layer is then lowered into the bath and the processis repeated for the generation of the next layer, until a plurality ofsuperimposed layers forming the desired part is obtained.

Even though three-dimensional fabrication is widely practiced and hasbecome a routine process for manufacturing three-dimensional objects, itis not without certain operative limitations that would best be avoided.

For example, in conventional three-dimensional fabrication techniquesthere is a discrepancy between the designed thickness and the finalthickness of the deposited layers. The discrepancy may be the result ofvarious factors, including continuous shrinkage process, incompatibilitybetween the resolution of the layer and its thickness, formation of“dead” areas in the layers and the like. This discrepancy oftentimesleads to a reduction in the accuracy of the final product.

Additionally, many of the presently known three-dimensional fabricationtechniques employ a leveling device which ensures that each layer of theobject is accurately leveled, but, at the same time, discards excessmaterial from the layer and a considerable amount of waste is producedat each leveling step.

There is thus a widely recognized need to have a method and system forthree-dimensional fabrication, devoid of the above limitations.

SUMMARY OF THE INVENTION

The background art does not teach or suggest a method and system forthree-dimensional layerwise fabrication in which post-formationshrinkage along a vertical direction, which is not constant over thevarious layers, is compensated.

The background art does not teach or suggest a method and system forthree-dimensional layerwise fabrication in which post-formationshrinkage along one or more horizontal directions, which depends on thetime length of layer formation, is compensated.

The background art does not teach or suggest a method and system forthree-dimensional layerwise fabrication which overcome problemsassociated with the planar and/or vertical resolution of the layers.

The background art does not teach or suggest a method and system forthree-dimensional layerwise fabrication which overcome problemsassociated with defective locations on the layers, except of randomscatter of nozzles from layer to layer.

Thus, according to one aspect of the present invention there is provideda method for three-dimensional fabrication of an object, by forming aplurality of layers in a configured pattern corresponding to the shapeof the three-dimensional object.

According to further features in preferred embodiments of the inventiondescribed below, at least one layer is formed at a predetermined anddifferent thickness, relative to other layers, and selected so as tocompensate for post-formation shrinkage of the layer along a verticaldirection.

According to still further features in the described preferredembodiments at least one layer is rescaled along at least one horizontaldirection so as to compensate for post-formation shrinkage of the layeralong the at least one horizontal direction.

According to still further features in the described preferredembodiments the formation time of the layer is kept constant for alllayers. According to still further features in the described preferredembodiments the constant formation time is achieved by scanning aprinting area that is as large as the area of one of the first layersfor all the layers.

According to another aspect of the present invention there is provided asystem for three-dimensional fabrication of an object. The systemcomprises a three-dimensional fabrication apparatus, designed andconstructed to form a plurality of layers in a configured patterncorresponding to the shape of the three-dimensional object.

According to still further features in the described preferredembodiments the three-dimensional fabrication apparatus has a controllerwhich ensures that (i) at least one layer is formed at a predeterminedand different thickness selected so as to compensate for post-formationshrinkage of the layer along a vertical direction, and/or (ii) at leastone layer is rescaled along at least one horizontal direction so as tocompensate for post-formation shrinkage of the layer along the at leastone horizontal direction.

According to still further features in the described preferredembodiments the rescaling along the at least one horizontal direction isa monotonically decreasing function of a formation time of a layer.

According to still further features in the described preferredembodiments the predetermined and different thickness is selected so asto compensate for cumulative post-formation shrinkage of the layer andat least one additional layer below the layer.

According to still further features in the described preferredembodiments the rescaling along the at least one horizontal direction isperformed so as to compensate for cumulative post-formation shrinkage ofthe layer and at least one additional layer below the layer.

According to still further features in the described preferredembodiments the predetermined and different thickness is a function of avertical position of the layer in the three-dimensional object.

According to still further features in the described preferredembodiments the function of the vertical position comprises at least oneexponentially decaying function of the vertical position.

According to still further features in the described preferredembodiments the predetermined and different thickness is a function of aformation time of the layer.

According to still further features in the described preferredembodiments the formation of the layers comprises: selectivelydispensing a layer of building material in a pattern mannerconfiguration; curing the layer of the building material; and repeatingthe step of selectively dispensing and the step of curing a plurality oftimes.

According to still further features in the described preferredembodiments the object is fabricated on a tray, and the formation of theplurality of layers comprises lowering the tray by a different step sizefor different layers.

According to still further features in the described preferredembodiments the layers are formed at a predetermined and differentthickness but assume the same thickness after the post-formationshrinkage.

According to still further features in the described preferredembodiments the formation of the layers comprises computing layers ofdifferent thickness.

According to still further features in the described preferredembodiments the formation of the layers comprises lowering the tray by aconstant step size for different layers.

According to still further features in the described preferredembodiments the rescaling is performed on digital data representing theobject.

According to still further features in the described preferredembodiments the rescaling is performed according to the formation timeof a predetermined layer, which can be, for example, one of the lowestlayers of the object.

According to still further features in the described preferredembodiments the rescaling is performed on digital data of the objectprior to slicing.

According to still further features in the described preferredembodiments the spread of building material per unit area in the layeris diminished at least locally.

According to still further features in the described preferredembodiments the diminishing is done so as to maintain the predeterminedthickness and a predetermined planar resolution of the layer.

According to still further features in the described preferredembodiments the spread of building material is diminished at interiorregions of the object, the interior regions being characterized by adistance from a closest exterior surface of the object which is above apredetermined threshold distance.

According to still further features in the described preferredembodiments the predetermined threshold distance is dependent on thespatial direction from the interior regions to the exterior surface.

According to still further features in the described preferredembodiments the spread of building material is diluted exclusively at aninner portion of the layer, to provide, for the layer, a central dilutedregion surrounded by a peripheral non-diluted region.

According to still further features in the described preferredembodiments the spread of building material is diminished such as toreduce amount of excess of building material removed as waste.

According to still further features in the described preferredembodiments the diminishing is obtained by diluting the spread ofbuilding droplets.

According to still further features in the described preferredembodiments at least one layer is characterized by a bitmap with respectto a predetermined horizontal reference frame.

According to still further features in the described preferredembodiments bitmaps of adjacent layers are interlaced with respect tothe predetermined horizontal reference frame.

According to still further features in the described preferredembodiments bitmaps of every two adjacent layers are defined withrespect to different horizontal reference frames.

According to still further features in the described preferredembodiments the formation of the layers is by a stereolithographytechnique.

According to still further features in the described preferredembodiments the three-dimensional fabrication apparatus comprises astereolithography apparatus.

According to still further features in the described preferredembodiments the formation of the layers comprises employing a powderbinding technique.

According to still further features in the described preferredembodiments the three-dimensional fabrication apparatus comprises apowder binding fabrication apparatus.

According to still further features in the described preferredembodiments the dispensing is by at least one nozzle array. According tostill further features in the described preferred embodiments defectivenozzles and non-defective nozzles in the nozzle array(s) are detectedprior to the formation of the layers, so as to allow compensation of thedefective nozzles during the dispensing step.

According to still further features in the described preferredembodiments the dispensing is performed in a manner such that for eachk+1 adjacent layers, defective sectors in the lowest layer of the k+1adjacent layers are overlapped with non-defective sectors in the other klayers of the k+1 adjacent layers.

According to a further aspect of the present invention there is provideda method of three-dimensional printing of an object using athree-dimensional fabrication apparatus having a printing tray and aprinting head configured to dispense building material through at leastone nozzle array characterized by an array resolution along an axistypically referred to as the Y axis. The method comprises: (a)calculating a bitmap defined with respect to predetermined horizontalreference frame, the bitmap describing at least one layer of thethree-dimensional object, and being characterized by a planar resolutionalong the Y axis which is substantially an integer multiplication of thearray resolution; (b) moving the printing head over the printing traywhile dispensing the building material according to the bitmap, therebyforming a layer compatible with the bitmap; and (c) repeating the steps(a) and (b) a plurality of times such as to form a plurality of layers,in a manner such that bitmaps of adjacent layers are interlaced alongthe Y axis with respect to the predetermined horizontal reference frame.

According to a further aspect of the present invention there is provideda method of three-dimensional printing of an object using athree-dimensional fabrication apparatus having a printing tray and aprinting head configured to dispense building material through at leastone nozzle array characterized by an array resolution along Y axis. Themethod comprises: (a) calculating a bitmap describing at least one layerof the three-dimensional object; (b) moving the printing head over theprinting tray while dispensing the building material according to everyi-th row of pixels in X direction of the bitmap, wherein the i is aninteger larger than one (e.g., i=2), thereby forming a layer compatiblewith the bitmap; and (c) repeating the steps (a) and (b) a plurality oftimes such as to form a plurality of layers, in a manner such that ineach layer the dispensed rows of pixels in X direction are interlacedalong Y axis in respect to adjacent rows.

According to yet a further aspect of the present invention there isprovided a system for three-dimensional printing of an object. Thesystem comprises: a three-dimensional fabrication apparatus having aprinting tray and a printing head configured to dispense buildingmaterial through at least one nozzle array characterized by an arrayresolution along the Y axis; and a data processor supplemented with analgorithm for calculating a bitmap defined with respect to predeterminedhorizontal reference frame, the bitmap describing at least one layer ofthe three-dimensional object, and being characterized by a planarresolution the Y axis which is substantially an integer multiplicationof the array resolution; the printing head being operatively associatedwith a controller designed and constructed to ensure that the printinghead repeatedly moves over the printing tray while dispensing thebuilding material according to the bitmap to form a plurality of layerseach being compatible with a respective bitmap, wherein bitmaps ofadjacent layers are interlaced with respect to the predeterminedhorizontal reference frame.

According to still a further aspect of the present invention there isprovided a system for three-dimensional printing of an object. Thesystem comprises: a three-dimensional fabrication apparatus having aprinting tray and a printing head configured to dispense buildingmaterial through at least one nozzle array characterized by an arrayresolution; a data processor supplemented with an algorithm forcalculating a bitmap defined with respect to predetermined horizontalreference frame, the bitmap describing one layer of thethree-dimensional object, and being characterized by a planar resolutionwhich is substantially an integer multiplication of the arrayresolution; the printing head being operatively associated with acontroller designed and constructed to ensure that the printing headrepeatedly moves over the printing tray while dispensing the buildingmaterial according to the bitmap to form a plurality of layers, whereineach layer is compatible with a respective bitmap and bitmaps of any twoadjacent layers are defined with respect to different horizontalreference frames.

According to still a further aspect of the present invention there isprovided a method of three-dimensional printing of an object using athree-dimensional fabrication apparatus having a printing tray and aprinting head configured to dispense building material through at leastone nozzle array. The method comprises: detecting defective nozzles inthe at least one nozzle array; repeatedly moving the printing head overthe printing tray while dispensing the building material to form aplurality of layers, at least one layer of the plurality of layershaving defective sectors corresponding to the defective nozzles andnon-defective sectors corresponding to non-defective nozzles, theplurality of layers being formed in a configured pattern correspondingto the shape of the three-dimensional object; the repeated moving beingperformed in a manner such that for each k+1 adjacent layers, defectivesectors in the lowest layer of the k+1 adjacent layers are overlappedwith non-defective sectors in the other k layers of the k+1 adjacentlayers.

According to still a further aspect of the present invention there isprovided a system for three-dimensional printing of an object. Themethod comprises: a three-dimensional fabrication apparatus having aprinting tray and a printing head configured to dispense buildingmaterial through at least one nozzle array, having defective nozzles andnon-defective nozzles; wherein the printing head is operativelyassociated with a controller designed and constructed to ensure that theprinting head repeatedly moves over the printing tray while dispensingthe building material to form a plurality of layers, at least one layerof the plurality of layers having defective sectors corresponding to thedefective nozzles and non-defective sectors corresponding to thenon-defective nozzles, the plurality of layers being formed in aconfigured pattern corresponding to the shape of the three-dimensionalobject; the controller being further designed and constructed to ensurethat for each k+1 adjacent layers, defective sectors in the lowest layerof the k+1 adjacent layers are overlapped with non-defective sectors inthe other k layers of the k+1 adjacent layers.

According to further features in preferred embodiments of the inventiondescribed below, k equals or is larger than 1.

According to still further features in the described preferredembodiments substantially all the defective sectors in the lowest layerof the k+1 adjacent layers are overlapped with non-defective sectors inthe other k layers of the k+1 adjacent layers.

According to still further features in the described preferredembodiments non-defective nozzles dispense an increased amount of thebuilding material on non-defective sectors overlapped with the defectivesectors.

According to still further features in the described preferredembodiments the non-defective nozzles are operated with increasedvoltage while moving above defective sectors.

According to still further features in the described preferredembodiments the non-defective nozzles dispense the building material atan increased planar density while moving above defective sectors.

According to still further features in the described preferredembodiments non-defective nozzles dispense at an increased jettingfrequency on non-defective sectors overlapped with the defectivesectors.

According to still further features in the described preferredembodiments the method comprises scanning the layers along the Xdirection, and the overlapping is ensured by shifting the printing headin the Y direction prior to the scan of each layer.

According to still further features in the described preferredembodiments the printing head is operable to scan the layer in the Xdirection, and the controller is designed and constructed to shift theprinting head in the Y direction prior to the scan of each layer, so asto ensure the overlapping.

According to still further features in the described preferredembodiments the shift in the Y direction is selected from apredetermined series of shifts.

According to still further features in the described preferredembodiments the shift in the Y direction is randomly selected from apredetermined series of shifts.

According to still further features in the described preferredembodiments the building material is curable by ultraviolet or visiblelight.

According to still further features in the described preferredembodiments the building material comprises photopolymer material.

According to still further features in the described preferredembodiments the system further comprises a radiation source for curingthe building material following dispensing a layer thereof and prior todispensing thereon of a succeeding layer of the building material.

According to still further features in the described preferredembodiments the system further comprises a temperature control unit forcontrolling the temperature in the system.

According to still further features in the described preferredembodiments the system further comprises at least one leveling devicefor leveling each layer prior to dispensing thereon of a succeedinglayer.

According to still further features in the described preferredembodiments the system further comprises a cooling unit for cooling thethree-dimensional object and/or three-dimensional fabrication apparatus.

According to still further features in the described preferredembodiments the system further comprises a sensing unit to determinecollisions or potential collisions between the printing head and thethree-dimensional object.

According to still further features in the described preferredembodiments the system further comprises a sensing unit to determinecollisions or potential collisions between the leveling device and thethree-dimensional object.

According to still a further aspect of the present invention there isprovided a method of preparing a bitmap for three-dimensional printingof an object, the bitmap corresponding to a predetermined resolution anda predetermined thickness of a layer of the object. The methodcomprises: preparing a preliminary bitmap according to the predeterminedresolution; calculating an expected thickness of the layer resultingfrom the preliminary bitmap; calculating a ratio between the expectedthickness and the predetermined thickness of the layer; based on theratio, applying a dilution transformation to the preliminary bitmap,thereby preparing the bitmap.

According to further features in preferred embodiments of the inventiondescribed below, the dilution transformation dilutes the spread ofbuilding material at interior regions of the object. The interiorregions can be characterized by a distance from a closest exteriorsurface of the object which is above a predetermined threshold distance.

The present invention successfully addresses the shortcomings of thepresently known configurations by providing a method and system forthree-dimensional fabrication.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Although methods and materialssimilar or equivalent to those described herein can be used in thepractice or testing of the present invention, suitable methods andmaterials are described below. In case of conflict, the patentspecification, including definitions, will control. In addition, thematerials, methods, and examples are illustrative only and not intendedto be limiting.

Implementation of the method and system of the present inventioninvolves performing or completing selected tasks or steps manually,automatically, or a combination thereof. Moreover, according to actualinstrumentation and equipment of preferred embodiments of the method andsystem of the present invention, several selected steps could beimplemented by hardware or by software on any operating system of anyfirmware or a combination thereof. For example, as hardware, selectedsteps of the invention could be implemented as a chip or a circuit. Assoftware, selected steps of the invention could be implemented as aplurality of software instructions being executed by a computer usingany suitable operating system. In any case, selected steps of the methodand system of the invention could be described as being performed by adata processor, such as a computing platform for executing a pluralityof instructions.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

The invention is herein described, by way of example only, withreference to the accompanying drawings. With specific reference now tothe drawings in detail, it is stressed that the particulars shown are byway of example and for purposes of illustrative discussion of thepreferred embodiments of the present invention only, and are presentedin the cause of providing what is believed to be the most useful andreadily understood description of the principles and conceptual aspectsof the invention. In this regard, no attempt is made to show structuraldetails of the invention in more detail than is necessary for afundamental understanding of the invention, the description taken withthe drawings making apparent to those skilled in the art how the severalforms of the invention may be embodied in practice.

In the drawings:

FIGS. 1a-1b are schematic illustrations of a system forthree-dimensional fabrication of an object, according to variousexemplary embodiments of the present invention;

FIGS. 2a-2c are schematic illustrations of a three-dimensional ink-jetprinting apparatus, according to various exemplary embodiments of thepresent invention;

FIG. 3a is a plot exemplifying typical variation in the thickness of alayer as a function of time;

FIG. 3b is a plot exemplifying the individual final thickness of each ofthe layers which form the object, from the lowest layer upwards;

FIG. 3c is a plot exemplifying the compensated initial thickness of alayer as a function of the time at which the layer is formed, accordingto various exemplary embodiments of the present invention;

FIGS. 4a and 4c are schematic illustrations of objects manufactured inaccordance with preferred embodiments in which the object is formed fromlayers of different sizes;

FIG. 4b is a plot exemplifying a typical form of the final thickness ofthe layers in FIG. 4a , according to various exemplary embodiments ofthe present invention;

FIG. 5 is a schematic illustration of a procedure for performing localdilution of a layer, according to various exemplary embodiments of thepresent invention;

FIGS. 6a-6b are schematic illustrations of a dilution transformation ofa bitmap of material droplets (or cells) in an exemplary embodiment inwhich a dilution of about 25% is employed;

FIGS. 7a-7d are side views of a formed layer with (FIGS. 7b and 7d ) andwithout (FIGS. 7a and 7c ) a peripheral denser region, before (FIGS.7a-7b ) and after (FIG. 7c-7d ) leveling, according to various exemplaryembodiments of the present invention;

FIGS. 8a-8b are schematic illustrations of a further procedure forperforming local dilution of a layer, according to various exemplaryembodiments of the present invention

FIG. 9 is a flowchart diagram of a preferred method for preparing abitmap of droplets corresponding to a predetermined resolution of alayer, according to various exemplary embodiments of the presentinvention;

FIG. 10 is a schematic illustration of a layer, a bitmap and a nozzlearray having defective nozzles;

FIG. 11 is a flowchart diagram of a method for three-dimensionalprinting of an object, according to various exemplary embodiments of thepresent invention; and

FIG. 12 is a schematic illustration of a procedure for increasing planardensity of building material that compensates for dead nozzles in apreceding layer, according to various exemplary embodiments of thepresent invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present embodiments comprise a system and method which can be usedfor three-dimensional layer-wise printing of an object. The presentembodiments can be used to provide three-dimensional objects havingenhanced dimensional accuracy. Specifically, the present embodiments canbe used to compensate for vertical discrepancies and/or defectivesectors in the layers of the object.

The principles and operation of a method and system according to thepresent embodiments may be better understood with reference to thedrawings and accompanying descriptions.

Before explaining at least one embodiment of the invention in detail, itis to be understood that the invention is not limited in its applicationto the details of construction and the arrangement of the components setforth in the following description or illustrated in the drawings. Theinvention is capable of other embodiments or of being practiced orcarried out in various ways. Also, it is to be understood that thephraseology and terminology employed herein is for the purpose ofdescription and should not be regarded as limiting.

The method and system of the present embodiments fabricatethree-dimensional objects in a layerwise manner by forming a pluralityof layers in a configured pattern corresponding to the shape of object.Each layer is formed by an apparatus which scans a two-dimensionalsurface and patterns it. While scanning, the apparatus visits aplurality of target locations on the two-dimensional layer or surface,and decides, for each target location or a group of target locations,whether or not the target location or group of target location is to beoccupied by building material in the final object. The decision is madeaccording to a computer image of the surface.

Generally, the information for producing the layers of the object can bedescribed in the form of two-dimensional bitmaps of the required spatialresolution in both X and Y directions. The bitmap corresponds to therequired printing plot, where each two-dimensional bitmap element (e.g.,pixel) corresponds to a target location that should be filled withbuilding material or left empty in the real printing plot. Such bitmapis translated to an operating bitmap, in which each bitmap elementcorresponds to a target location on the respective layer on which asingle smallest-quanta of material is deposited. In the simplest case,the bitmaps store binary information where, for example, “1”s representlocations which are to be occupied by building material in the finalobject and “0”s represent voids in the final objects.

For example, when an ink-jet head is used for ejecting a buildingmaterial, “1”s in an operating bitmap can represent locations on whichthe ink-jet head ejects one single droplet per pixel and “0”s representlocations skipped by the ink-jet head. On the other hand, “1”s in anon-operating bitmap can represent locations on which the ink-jet headejects one or more droplets per pixel. The bitmap and the operatingbitmap can either coincide or they can differ.

More sophisticated bitmaps in which the bitmap elements can storenon-binary values (representing, e.g., local amounts of buildingmaterial) are also contemplated. A target location on a layer which isoccupied by building material (corresponding, for example, to a “1” inthe respective bitmap element) is referred to herein as an “occupiedlocation” and a location which is to be left unoccupied (corresponding,for example, to a “0” in the respective bitmap element) is referred toas a “void location”.

The three-dimensional fabrication apparatus can operate in many ways.For example, referring to the above “1” and “0” binary convention, theapparatus can dispense building material in target locations whichcorrespond to “1”s in the bitmap, and leave voids in target locationswhich correspond to “0”s in the bitmap. Similarly support material canbe dispensed corresponding to “1”s in the support bitmap. In anotherembodiment, the bitmap may store tertiary information, where buildingmaterial can be dispensed in target locations corresponding to “2”s inthe bitmap and support material in target locations corresponding to“1”s, leaving voids in the target locations corresponding to “0”s in thebitmap.

Once the building and support materials are dispensed they are cured tostabilize the newly formed layer. The supporting matrix, which is oftencomposed primarily of the second type of material reinforced with minutematerial of the first type (in either continuous form or as discreteelements such as pins and membranes) can be removed (e.g., by washing)once the layer is formed, or, more preferably, after the printing of theobject is completed.

In other embodiments, the layer can be made of uniform material and thefabrication apparatus can selectively transform, for example, bybonding, curing or solidifying, the building material according to thebitmap, thus forming on the layer target locations having a first typeof material and target locations having a second type of material. Thematerial in the target locations corresponding to “0”s is preferablyremovable, so as to allow its removal either once the layer is formed orafter the fabrication of the object is completed.

The formation of every layer is thus accompanied by a process in whichthe layer is solidified, bonded or cured, which is typicallyaccomplished in an environment of elevated temperatures. Each layer(except the first) is formed or laid on a previously formed layer.

The present embodiments successfully provide solutions to severalproblems associated with three-dimensional printing.

One such problem relates to post-formation shrinkage of the layers in Zdirection (or decrease of layers' thickness). Due to the gradualreduction in temperature in the lower layers and the continuation of theformation process of the upper layers, there may be continuous Zshrinkage of the layers for a period of time following their formation.The shrinkage of layers has a cumulative impact on the thickness ofsuccessive layers, because during the time in which a successive layeris formed, its supporting area may sink.

Post-formation shrinkage occurs in many three-dimensional printingtechniques, and reduces the printing accuracy of the final printedobject, because in reality the thickness of the layers is lower than thedesigned thickness. Such discrepancy may also affect the overalldimensions of the printed object. As explained in greater detailhereinunder, the system and method of the present embodiments form eachlayer of the object at a thickness selected to compensate for thepost-formation shrinkage. Two embodiments are presented for suchcompensation. In a first such embodiment, each Z step of the tray fromlayer to layer has a different value, which is preferably characterizedby a decreasing function of a vertical position of the layer in theobject. In a second embodiment, the Z step is maintained constant, whilethe computation of the layers (object slicing) assumes layers ofdifferent thickness, preferably characterized by an increasing functionof a vertical position of the layer in the object.

Another problem associated with three-dimensional printing relates tothe planar resolution of the layers. The planar resolution of the layersis defined as the number of target locations on the surface of the layerper unit area. When the planar resolution of the layers is notcompatible with the type of building material and/or the inherentresolution of the printing apparatus, undesired variations may occur inthe thickness of the layers. Specifically, too high a planar resolutionmay result in formation of a thicker layer than desired and too low aplanar resolution may result in formation of a thinner layer thandesired. As further detailed hereinunder, the system and method of thepresent embodiments successfully overcome this problem by judiciousbitmap manipulations.

An additional problem, typically associated with types of printingapparatus which dispense building materials through nozzle arrays,relates to the formation of defective locations on the layer. Thisproblem is addressed by the present embodiments by increasing the amountof building material in regions of the subsequent layer which overlapthe defective locations, as further detailed hereinafter.

Referring now to the drawings, FIGS. 1a-1b illustrate a system 10 forthree-dimensional fabrication of an object 12, according to variousexemplary embodiments of the present invention. System 10 comprises aprinting apparatus 14 which forms a plurality of layers 16 in aconfigured pattern corresponding to the shape of object 12.

It is to be understood that although the layers illustrated in FIG. 1aare of substantially equal surface area, this need not necessarily bethe case, since, for some objects, it may not be necessary for thelayers to have equal surface area. An exemplary embodiment in whichlayers 16 have non-uniform size is described hereinunder (see FIG. 4aand the accompanying description).

In a preferred embodiment, apparatus 14 comprises a layer-forming head13 for forming layers 16 and a tray 15 which carries layers 16 as theyare formed. Head 13 may form layers by any known technique, including,without limitation, ink-jet printing, as further detailed hereinunder.In various exemplary embodiments of the invention head 13 comprises acomposite array 17 of forming units 19, such as to allow head 13 tosimultaneously address several target locations on the formed layer. Asfurther detailed hereinunder, units 19 can be nozzles or radiationsources, depending on the technique employed for forming the layers.Layer-forming head 13 may comprise a number of separate printing heads,each having an array of forming units 19, but for ease of presentation,a single composite array 17 of forming units 19 is shown in FIG. 1 b.According to the common conventions, units 19 are arranged along the Ydirection, each layer is formed while performing one or more scans ofhead 13 along the X direction, and the formed layers are stacked alongthe Z direction.

Apparatus 14 preferably comprises a controller 18 which controls theoperation of apparatus 14 to ensure that the layers are properly formed.Specifically, controller 18 ensures that each layer is formed at apredetermined and optionally different thickness, selected so as tocompensate for post-formation shrinkage of the layer along a verticaldirection.

As used herein in the specification and the claims section that follows,“post-formation shrinkage” refers to shrinkage of the layer during atime period which begins subsequently to, and immediately after, theformation of the layer, and ends when the changes in the volume of thelayer are negligible (preferably less than 0.1%). Such time period isreferred to herein as the “post-formation period.” When several stepsare required for forming the layer the post-formation period begins, inmost cases, immediately after all the steps are completed. For example,when the formation of the layer includes dispensing a building materialfollowed by leveling, the post-formation period begins immediately afterthe leveling step. In some cases, the post-formation period of one layerbegins contemporaneously with the beginning of the formation of thesubsequent layer.

Representative examples of methods to determine the suitable thicknessesof the layers are provided hereinunder.

Controller 18 may be located either within apparatus 14 or it cancommunicate externally therewith via wire and/or wireless communication.Controller 18 preferably comprises, or operates in combination with, adata processor 20 which transmits building instructions to controller18, based on, for example, a predetermined CAD configuration which maybe converted, for example, to a Solid Triangulated Language (STL) or aSlice (SLC) format used by the data processor.

Supporting software in processor 20 use computer object datarepresenting the desired dimensional configuration of object 12 andtransmits building instructions to be executed by controller 18.Specifically, a suitable algorithm in the supporting software createsthe geometry of the object, and slices the geometry into the desirednumber of layers. Each layer is preferably described in a form ofbitmaps as further detailed hereinabove.

Apparatus 14 typically comprises motion devices which are responsive tosignals transmitted by controller 18. These motion devices operate toestablish relative translational motions between the layer-forming headand tray 15 or the upper surface of the object (also referred to as“work surface”), both in the plane of tray 15 or the work surface(conventionally defined as the X-Y plane, see, e.g., FIG. 1b ), and inthe vertical direction (conventionally defined as the Z direction, see,e.g., FIG. 1 a). Apparatus 14 can be any three-dimensional fabricationapparatus known in the art, including, without limitationstereolithography, powder binding and fused deposition modeling.

In various exemplary embodiments of the invention, apparatus 14 formsthe layers by selectively dispensing the building material and curingthe building material following the dispensing thereof and prior to thedispensing of the successive layer thereon. This type of apparatus isreferred to as ink-jet printing apparatus and is described, e.g., inU.S. Pat. Nos. 6,259,962, 6,569,373, 6,658,314, 7,183,335, 6,850,334,and 6,863,859, U.S. patent application Ser. Nos. 10/716,426, 09/484,272,10/336,032, 11/433,513, US Publication No. 2005/0069784 and PCTPublication No. WO/2004/096527, all assigned to the common assignee ofthe present invention and fully incorporated herein by reference.

A representative example of three-dimensional ink-jet printing apparatus14 is schematically illustrated in FIGS. 2a -2 c, for the preferredembodiment in which apparatus 14 selectively dispenses the buildingmaterial to form the layer.

In various exemplary embodiments of the invention apparatus 14 comprisesone or more printing heads 21 having one or more nozzle arrays 22,through which building material 24 is dispensed. Printing heads 21 serveas layer-forming heads. Apparatus 14 can further comprise one or moreradiation sources 26, which can be, for example, an ultraviolet orinfrared lamp, depending on the building material being used. Radiationsource 26 serves for curing the building material.

Printing head 21 and radiation source 26 are preferably mounted on aframe 28 operative to reciprocally move along a tray 30, which serves asthe working surface. According to the common conventions tray 30 ispositioned in the X-Y plane. Tray 30 is configured to move vertically(along the Z direction), typically downward. In various exemplaryembodiments of the invention, apparatus 14 further comprises one or moreleveling devices 32 which can be manufactured as a roller 34 or a blade.Leveling device 32 can be similar to the leveling device disclosed inU.S. Published Application No. 20050104241. Leveling device 32straightens the newly formed layer prior to the formation of thesuccessive layer thereon. Leveling device 32 preferably comprises awaste collection device 36 for collecting the excess material generatedduring leveling. Waste collection device 36 may comprise any mechanismthat delivers the material to a waste tank or waste cartridge.

Preferably, apparatus 14 comprises a sensing device 44 which may be, forexample, embedded within leveling device 32 or may be external thereto.Sensing device 44 serves to determine whether a collision with object 12has occurred or is expected to occur. Such a collision may be, forexample, as a result of dispensed layers being too thick and/orinconsistent in thickness, and/or because of a mechanical malfunction ofthe printing head. Collision may also occur as a result of materialspill or faulty material dispensing that may occur anywhere in the pathof the printing head. For example, sensing device 44 may be or includean acceleration-sensing device, a shock sensor and the like.

According to a preferred embodiment of the present invention, apparatus14 further comprises a cooling unit 38 for cooling object 12 and orapparatus 14. Unit 38 may comprise a blowing unit and/or a sucking unit,for respectively cooling apparatus 14 by sucking hot air or othersubstances out of apparatus 14 and/or drawing cool air or othersubstances in to apparatus 14 from the surroundings.

In use, printing head 21 moves in the X direction and dispenses thebuilding material in the course of its passage over tray 30, in apredetermined configuration. The passage of head 21 is followed by thecuring of the deposited material by radiation source 26. In the reversepassage of head 21, back to its starting point for the layer justdeposited, an additional dispensing of building material may be carriedout, according to predetermined configuration. In the forward and/orreverse passages of head 21, the layer thus formed may be straightenedby leveling device 32, which preferably follows the path of head 21 inits forward and/or reverse movement.

Leveling device 32 provides more than one improvement to the newlyformed layer. Firstly, leveling device 32 ensures uniform and accuratelayer height. Secondly, leveling device 32 eliminates undesired patternsin the form of grooves or ridges which may be caused by defectivenozzles in printing head 21. Thirdly, leveling device 32 sharpens theedge of the newly formed layer, such that droplets of building materialof the subsequent layer can be deposited at the proper target locationon the leveled layer.

The operation of leveling device 32 is better illustrated in FIG. 2 c,showing a newly formed layer 16 a and a few previously formed layers 16b, where layers 16 b are already leveled and cured and layer 16 b isbeing leveled by device 32 which moves in a direction generally shown as33. As shown, once layer 16 a is formed it has generally round edges,which are subsequently sharpened by device 32. A round edge and asubstantially sharper edge are illustrated in FIG. 2c as 35 and 37,respectively. While contacting the newly formed layer, device 32discards from the layer excess material 39 which is collected by wastecollection device 36.

Once head 21 returns to its starting point along the X direction, it maymove to another Y position and continue to build the same layer byreciprocal movement along the X direction. Once the layer is completed,tray 30 is lowered in the Z direction to a predetermined Z level,according to the desired thickness of the layer subsequently to beprinted. The procedure is repeated to form three-dimensional object 12in a layerwise manner.

In another embodiment, tray 30 may be displaced in the Z directionbetween forward and reverse passages of head 21, within the layer. SuchZ displacement is carried out in order to cause contact of the levelingdevice with the surface in one direction and prevent contact in theother direction.

While the above description of apparatus 14 places a particular emphasison embodiments in which the layers are formed by selective dispensingand curing of building material, it is to be understood that moredetailed reference to such technique is not to be interpreted aslimiting the scope of the invention in any way. For example, otherpractitioners in the field form the layers by stereolithography, powderbinding and fused deposition modeling (to this end see, e.g., in U.S.Pat. Nos. 4,575,330 and 5,204,055 supra).

Thus, also contemplated are embodiments in which apparatus 14 comprisesa stereolithography apparatus. As previously indicated,stereolithography is a method and apparatus for three-dimensionalprinting of solid objects by successively forming thin layers of acurable material one on top of the other. A programmed movable spot beamof curing radiation on a surface or layer of curable fluid medium isused to form a solid layer of the object at the surface of the liquid.In a preferred embodiment, the curable fluid medium is an ultravioletcurable liquid and the curing radiation can be ultraviolet light. Once asolid layer of the object is formed, the layer is moved, in a programmedmanner, away from the fluid surface by the thickness of one layer andthe next cross-section is then formed and adhered to the immediatelypreceding layer defining the object. This process is continued until theentire object is formed.

Layer-forming head 13 of apparatus 14 may thus comprise a source ofultraviolet light which produces a spot of ultraviolet light on thesurface of the curable liquid and moves it across the surface, forexample, by the motion of mirrors or other optical or mechanicalelements. The interaction between the curable liquid and the ultravioletlight results in solidification at their point of interaction. As thespot moves on the surface, a layer is formed. An elevator platform canbe used to move the previously formed layer to a different (e.g., lower)location prior to the formation of the subsequent layer.

In another embodiment, apparatus 14 builds each layer of object 12 byspreading a layer of a powder material in a confined region, andapplying a binder material to selected regions of the layer to therebybond the powder material in the selected regions. In this embodiment,layer-forming head 13 of apparatus 14 may comprise a mechanism forspreading the powder material and another mechanism for dispensing thebinder material. The powder material can be, for example, a ceramicpowder. The binder material can be any material, organic or inorganic,known in the art which is capable of performing binding action betweenthe particles of the powder material. The mechanism for spreading thepowder can include a powder dispersion head which moves reciprocallywhile dispensing the powder material. The mechanism for dispensing thebinder material can be in a form of several ink-jet dispensers whichmove in the same reciprocal manner so as to follow the motion of thepowder head. The ink-jet dispensers selectively jet liquid bindermaterial at selected regions, thereby causing the powdered material inthese regions to bond. The powder/binder layer forming process isrepeated so as to form the object in a layerwise manner.

As stated, controller 18 receives instructions from data processor 20 toensure that each layer of the three-dimensional object is formed at apredetermined and optionally different thickness, such thatpost-formation shrinkage is compensated for. The shrinking process ofthe layers typically decreases with time.

Each time a layer is completed, the tray (or the printing head, togetherwith leveling apparatus) is preferably displaced in Z direction. Thismechanical step between layers is referred to hereinafter as a “Z step”.In addition, tray 30 may be displaced in Z direction between forward andreverse X movements of the printing head.

FIG. 3a exemplifies typical variation in the thickness, D_(i)(τ), of theith layer as a function of time after being formed, τ. The functionD_(i)(τ) can be conveniently defined as:

D _(i)(τ)=D _(0,i)[1−a(1−Exp(−τ/b))]  (EQ. 1)

where, D_(0,i), a and b are constant parameters, which depend on theprocess employed for forming the layer. D_(0,i), the initial layerthickness, is not necessarily equal to the Z step because of theshrinkage of former layers during the formation of the new layer.Conditions which affect the value of the parameters include, withoutlimitation, the initial thickness, the type of building material and thetype and duration of the curing, bonding or solidifying process. Otherconditions include, without limitation, the duration and type ofleveling process, if employed. In the plot of FIG. 3 a, the followingvalues for the parameters were used: D_(0,i)=30 μm, a=1.5 μm, b=10 min.As will be understood by one of ordinary skill in the art, the parameterb is the time-constant of the shrinkage process. For times much shorterthan b, the layer's thickness varies rapidly, and for times much longerthan b, thickness varies mildly or does not vary at all.

In three-dimensional printing processes in which the layer is formed bydispensing building material, leveling and curing it thereafter, asingle layer is typically formed within a time-interval, Δt, which isfrom about 1 second to about 30 seconds. Δt is referred to herein as aformation time or a duration.

As used herein the term “about” refers to ±10%.

With Δt, which is considerably shorter than the aforementionedtime-constant (10 minutes in the above example), the layer may continueto shrink for a period of time after its formation. Except for thelayers at the very bottom of the object, newly formed layers are thusformed on layers which are liable to shrink during the time between thelast layer leveling and the leveling of the new layer (Δt). Hence thethickness of the new layer just after being leveled is larger than thecontrolled Z step. As time elapses, the layer becomes thinner due to itsown shrinkage. As a consequence, the thickness of the higher layers isgreater than the thickness of the lower layers. In sufficiently highlayers, the two effects of shrinking (the cumulative shrinking of thelayers below, and the shrinking of the new layer itself) compensate eachother and the layer thickness approaches the Z step.

FIG. 3b exemplifies the individual final thickness of each of theplurality of layers forming the object, from the lowest layer upwards.In FIG. 3 b, the ordinate of the plot represents the final thicknessD_(t) of layers and the abscissa of the plot represents the layer serialnumber expressed in terms of the elapsed time t from start of print ofthe object to the time of layer formation. Thus, in the abscissa of FIG.3 b, the value of t=0 corresponds to the lowest layer, and the value oft=50 minutes corresponds to the upper layer (formed 50 minutes after thelowest layer).

Using the exemplified expression of Equation 1, for a uniform Z step=D₀,the final thickness D_(t) of the layers can be written as:

D _(t) =D ₀ −a Exp(−τ/b).  (EQ. 2)

The following describe ways to deal with the layer shrinkage, accordingto various exemplary embodiments of the present invention.

In one preferred embodiment, Z step (which may be a function of Z or,equivalently, t), of each layer is selected such that the finalthickness D_(t) of all the layers is as originally desired (e.g.,substantially uniform thickness). In this embodiment, the supportingsoftware, which slices the object into layers, regards the layers ashaving constant thickness. The layers are preferably formed at aninitial thickness that complements the later shrinkage.

Mathematically such procedure can be written as follows:

Z step=D_(c,t,)  (EQ. 3)

where D_(c,t) represents the compensated Z step of the layer formed attime t after print start. It may be worthwhile noting again that due tothe sequential nature of the three-dimensional printing process, thevertical positions of the layers correlate with the times at which theyare formed.

According to a preferred embodiment of the present invention each layeris formed at a predetermined and different Z step characterized by oneor more decaying functions of the vertical position (or, equivalently,the formation time) of the layer. The decaying functions are preferably,but not obligatorily, exponentially decaying functions. A singledecaying function is favored when the layers of the formed object are ofsubstantially uniform size, and two or more decaying functions arefavored for more intricate objects, as further detailed hereinunder.

A representative example of a single exponentially decaying function,according to a preferred embodiment of the present invention is:

D _(c,t) =D ₀ +a Exp(−t/b),  (EQ. 4)

where, similarly to Equation 2, the layer serial number is expressed interms of the elapsed time, t, from start of print.

Knowing the thickness and formation time of each layer, one ordinarilyskilled in the art would know how to construct a function Z(t)converting the temporal variable t to the spatial variable Z. Forexample, neglecting the difference between D₀ and D_(t), for layers ofuniform formation time-interval, Δt, and Z(t)=D₀(t/Δt). For the purposeof converting t to Z in Equation 4, the approximation D₀=D_(t) isemployed.

The present embodiments thus compensate for the post-formation shrinkageof the layer.

Replacing Do in Equation 2 by D_(c,t) per Equation 3, and substitutingthe expression of D_(c,t) per Eq. 4, one gets

D _(t)(t)=D _(c,t) −a Exp(−t/b)=D₀.  (EQ. 5)

Hence, the parameter D₀ in Equation 4 represents the final thickness ofthe layers. The shape of D_(c,t) for the aforementioned values of D₀, aand b is shown in FIG. 3 c.

In another preferred embodiment of the present invention, the supportingsoftware which slices the object into layers, refers to the thickness ofthe layer according to the actual final size D_(t), e.g., per Equation2. In this embodiment, a constant Z step, D₀, is used for the verticalmotion.

When the object is formed from layers of different X-Y sizes, theirtypical formation time intervals Δt also differ. In this embodiment, thefunction D_(c)(t) is preferably a combination of several decayingfunctions, such as, but not limited to, exponentially decayingfunctions.

Reference is now made to FIG. 4a which is a schematic illustration ofobject 12 in the preferred embodiment in which object 12 is formed fromlayers of different sizes. Shown in FIG. 4a are small layers 16 a formedon top of large layers 16 b. The formation time interval of the smalllayers is shorter than the formation time interval of the large layers.As a result, at the beginning of the formation of the group of smalllayers the shrinkage is more pronounced. This is because at a higherlayer (having a greater Z value) the shrinking process of the layerafter being dispensed and cured tends to be balanced by the accumulatedshrinkage of lower layers during the time Δt between leveling before andafter dispensing the layer. For small layers Δt is smaller than forlarge layers. Therefore, although the last large layer (having large Δt)is, for example, near balance, balancing is not achieved at thebeginning of the formation of the small layer group, due to the smallerΔt. In small layers Δt is smaller and therefore, initially, thebalancing is not sufficient. After more small layers (more than requiredin large layers) the balancing is sufficient.

The final thickness D_(t) of the layers of FIG. 4a can be written as:

$\begin{matrix}{D_{t} = \{ {\begin{matrix}{D_{0} - {a_{1}{{Exp}( {{- t}\text{/}b_{1}} )}}} & {t < t_{1}} \\{D_{0} - {a_{2}{{Exp}( {{- t}\text{/}b_{2}} )}}} & {t > t_{1}}\end{matrix},} } & ( {{EQ}.\mspace{14mu} 6} )\end{matrix}$

where t₁ represents the time at which the formation of the small layersbegins, a₁, b₁ are constant parameters corresponding to the formation oflayers 14 a, and a₂, b₂ are constant parameters corresponding to theformation of layers 14 b. In various exemplary embodiments of theinvention b₂ approximately equals b₁. Note that the expression for t>t₁)is an approximation. This is because the lower layers of a small layercomprise a varying mix of large and small layers, and therefore thenature of their accumulated shrinkage during said time Δt graduallyvaries from one small layer to another small layer. For example, duringthe period Δt of the initial small layers, the accumulated shrinkage issubstantially due to the large lower layers, while for later smalllayers, the accumulated shrinkage of the lower layers is substantiallydue to small layers. Hence, the initial small layers are expected tobehave according to one exponential expression while the much latersmall layers behave according to another exponential expression.

FIG. 4b shows a typical form of the final thickness D_(t) of the layersin FIG. 4 a. For more than two different sizes (and formation timeintervals), the function D_(t) can comprise more decaying functions.

According to the presently preferred embodiment of the invention, thefunction D_(c,t) which, as stated, represents the compensated Z step ofthe layer, can be written as:

$\begin{matrix}{D_{c,t} = \{ {\begin{matrix}{D_{0} + {a_{1}{{Exp}( {{- t}\text{/}b_{1}} )}}} & {t < t_{1}} \\{D_{0} + {a_{2}{{Exp}( {{- t}\text{/}b_{2}} )}}} & {t > t_{1}}\end{matrix}.} } & ( {{EQ}.\mspace{14mu} 7} )\end{matrix}$

As will be appreciated by one of ordinary skill in the art, the functionD_(c,t) substantially compliments the function D_(t), hence compensatingfor the post-formation shrinkage.

Once the printing is finished, all the layers may continue to shrink inX, Y and Z directions due to the process of cooling from the temperatureof the object during printing to room temperature. According to apreferred embodiment of the present invention this shrinkage iscompensated for by performing a global rescaling in the horizontaland/or vertical directions. Rescaling in the horizontal and verticaldirections can be achieved by stretching the image of the object in therespective directions before slicing. Rescaling in the verticaldirection can alternatively be achieved either in the printing stage, byrescaling the step size of the working surface (Z step); or in theslicing stage, by rescaling the designed thickness of the layers.

The required scale correction in Z direction after the printingfinishes, as well as similar scale correction in X and Y directions,depend on the formation duration of the layers. Although the heatgenerated and absorbed at each point of the layer does not depend on theformation duration, the cooling amount of the layer is proportional tothe formation duration. Therefore the longer the formation duration, thecooler the layer is. Hence, objects of long layer formation time arecooler than objects of short layer formation time after the printingfinishes, and therefore the former contract less than the latter aftercooling to room temperature. The contraction factor may differ for X, Yand/or Z directions. In particular global contraction in Z is preferablysmaller than in X-Y. This is because part of the contraction in Z (fromthe very first high temperature of a newly built layer to the steadystate temperature of the object during building) is constantlycompensated by the leveling apparatus and constant Z step duringbuilding. The contraction in the X-Y direction, on the other hand, takesplace consistently from the initial temperature of a newly built layeruntil the object cools to room temperature.

For example, for layer formation duration of 30 seconds the preferredglobal rescaling factor in the vertical direction is about +0.18% andthe preferred global rescaling factor in the horizontal direction isabout +0.26%, while for formation duration of 4 seconds the preferredglobal rescaling factor in the vertical direction is about +0.2% and thepreferred global rescaling factor in the horizontal direction is about+0.3%.

The global rescaling factor is preferably a monotonically decreasingfunction, e.g., a linear function, of its formation time Δt. Therescaling factor S is preferably defined as:

S=S ₀ cΔt,  (EQ. 8)

where S₀ and c are predetermined parameters and c<0.

When the layer is rescaled along two different directions, a differentrescaling factor can be used along each direction. For example, when theobject dimensions are rescaled along the X and Y direction, therescaling factors can be S_(x)=S_(0,x)+c_(x)Δt, andS_(y)=S_(0,y)+c_(y)Δt, respectively.

In case of layers with changing size from layer to layer, globalrescaling in X-Y in a given direction can be computed and performed perlayer. For a particular layer i the layer can be rescaled by a rescalingfactor, S_(i), which is preferably defined as:

S _(i) =S ₀ +cΔt _(i),  (EQ. 9)

where S₀ and c are predetermined parameters. In such case the center ofmass of the layer after rescaling is preferably at the same location asbefore rescaling.

The coefficients S₀ and c are preferably the same in both X and Ydirections, because they reflect the generally isotropic characteristicsof the building material. Alternatively, the global horizontal rescalingfactors can be written in the form S_(i,x)=S_(0,x)+c_(x)Δt_(i) for thehorizontal rescaling along the X direction andS_(i,y)=S_(0,y)+c_(y)Δt_(i) for the horizontal rescaling along the Ydirection.

Different rescaling factor S_(i) for different layers may, however,reduce the smoothness of vertical surface of the object. This isespecially the case when the parameter S₀ of Equation 9 is positive andthe parameter c is negative. In such situations, a single globalhorizontal rescaling factor S is preferred. A representative example ofsuch situation is illustrated in FIG. 4 c, showing object 12 with alower small part 11 a, an upper large part 11 b. Also shown are sidewalls parallel to the Y-Z plane (generally shown at 42 and referred toas “X-walls”) and side walls parallel to the X-Z plane (generally shownat 43 and referred to as “Y-walls”). When fabricating an object havingsuch or similar shape, the scale S_(i) in upper part 11 b is larger thanin lower part 11 a. After rescaling, the layers in the upper part ofsuch objects are larger in the X direction than the layers in the lowerpart. As a consequence, when the fabrication machine is, for example, aninkjet printing apparatus, the peripheral droplets in the X direction ofthe upper part may lack any support and tend to drip when printed. Someof these peripheral droplets may adhere to the X-walls of the objectwhile others may fall on the tray. The final product in this case wouldtherefore have inaccurate and unsmooth X-walls. The use of the sameglobal horizontal rescaling factor for all the layers in accordance withthe presently preferred embodiment, although not assuring the veryabsolute dimensions of all the object's parts, substantially preventsthe above effect, because in this embodiment substantially all theperipheral non-void target locations of substantially all layers arewell supported by non-void target locations of lower layers (or by thetray).

A single global horizontal rescaling factor can be determined from theformation duration of one of the layers (e.g., the first formed layer)using, e.g., the linear function of Equation 9 above. Once determined,this horizontal rescaling factor can be used as a global horizontalrescaling factor for all layers. Thus, according to the presentlypreferred embodiment of the invention the global horizontal rescalingfactors are S_(x)=S_(0,x)+c_(x)Δt₁ for the horizontal rescaling alongthe X direction and S_(y)=S_(0,y)+c_(y)Δt₁ for the horizontal rescalingalong the Y direction, where Δt₁ is the dispensing time of onepredetermined layer (such as, but not limited to, the first layer).

A possibility to overcome the need for different scale factors indifferent layers, which according to the discussion above cannot be met,may be as follows: According to an embodiment of the present invention,Δt (the layer's formation time) is kept constant for all the layers.This can be done, for example, by adding a pause between small layers,so as to have the same Δt for small layers as for the larger layersbelow (the layer below is always equal to or larger than the currentlayer). The pause may, for example, include scanning a printing areathat is as large as the area of the first (lowest) layer for all thelayers. In this way, though fabrication time of the object increases,the dimensions of all object's parts may become accurate. An additionaladvantage of this embodiment is reducing object deformation broughtabout by different shrinkage of layers, when the layers are formed atdifferent formation duration.

The present embodiments successfully address the problems associatedwith the planar resolution of the layers in three-dimensional printing.

It is appreciated that when a layer is formed, the thickness of thelayer depends on the volume of building material in each occupied targetlocation (e.g., an ejected material droplet) on the layer and on thedensity of the occupied target locations. For example, suppose forsimplicity that the layer is formed according to a rectangular bitmap inwhich the bitmap elements are arranged in n rows (arranged, say, alongthe Y direction) and m columns (arranged, say, along the X direction).Suppose further head 15 of printing apparatus 14 scans the layer alongthe X direction and is configured to simultaneously form the n rows in asingle scan (this can be achieved, for example, using a printing headhaving an array of at least n nozzles arranged along the Y direction,see, e.g., FIG. 1b ).

Typically, layers are defined as being composed of a continuous spreadof material. Therefore, for a given volume of building material at eachoccupied target location, and given material tendency to spread on theworking surface, there is a minimal density of the rows and a minimaldensity of the columns which can be defined without causing vacantspaces between the building materials of two adjacent occupied targetlocations. Once the density is above the minimal density, the buildingmaterial can be “piled” and affect the layer thickness or the verticalresolution of the three-dimensional object. If, for example, the densityof rows reaches its minimal value, the layer thickness is a function ofthe density of columns.

In various exemplary embodiments of the invention, controller 18 ensuresthat each layer is formed at a predetermined thickness and apredetermined planar resolution. For simplicity of explanation, theplanar resolution and the density of material droplets are treatedequivalently. More specifically, each planar pixel is regarded ascontaining (or devoid of) one single material droplet. When the planarresolution exceeds certain height limits, predetermined thickness ispreferably achieved by diminishing the spread of building material perunit area in the layer. In this way both the desired thickness and thedesired planar resolution are maintained.

According to a preferred embodiment of the present invention, thediminishing is not performed around the rim of the layer, where therequired planar resolution should be preserved. The diminishing isparticularly useful when it is desired to increase the resolution in theX direction. The spread of building material per unit area is thereforediminished so as to compensate for any increment in the layer'sthickness which may occur as a result of the increased resolution. Thedismissing can be done by diluting the spread of building material, byreducing the size of droplets, and the like.

According to a preferred embodiment of the present invention, the extentby which the spread of building material per unit area is diminishedequals the relative increment in thickness which would occur if nodiminishing is employed. For example, suppose that the diminishing isdone by dilution. and that the increased resolution results in a 25%increment in layer's thickness from desired resolution. In this case, a25% dilution of building material per unit area can compensate for suchthickness increment and maintain the desired thickness of the layer. Aswill be appreciated by one ordinarily skilled in the art, such dilutionallows formation of layers at high resolution.

Reference is now made to FIG. 5 a, which is a schematic illustration ofa procedure for performing local dilution of layer 16. According to thepresently preferred embodiment of the invention the local dilution isperformed by diluting the spread of building material exclusively at aninner portion of layer 16, thereby providing a central diluted region 52surrounded by a peripheral denser region 54.

The dilution is preferably performed by controller 18 or data processor20 at the bitmap level. Specifically, the bitmap of the respective layeris subjected to a dilution transformation such as to reduce the amountof building material in the regions which are to be diluted. Forexample, regions of “1”s in the bitmap of the respective layer areredefined such that the value of one or more bitmap elements in theregions is replaced from a “1” to a “0”. FIGS. 6a-6b schematicallyillustrates a dilution transformation of a bitmap in an exemplaryembodiment in which a dilution of about 25% is employed. Shown in FIGS.6a-6b is a portion of a bitmap 60 before (FIG. 6a ) and after (FIG. 6b )the dilution transformation was performed. As shown, the dilutiontransformation replaces every fourth “1” in the bitmap by a “0”, therebyproviding a diluted portion of the bitmap and a corresponding dilutedregion on layer 16.

Preferably, the dilution procedure is performed substantially evenly andat a substantially fine resolution so as to enable the building materialto flow into the vacant target location. In various exemplaryembodiments of the invention a different dilution transformation is usedfor different layers to reduce or eliminate accumulated holes in thelayers. The variations between dilution transformations across thelayers can be random or according to a predetermined rule.

The width W of region 54 can equal a width of a single target locationon layer 16 (corresponding to a single bitmap element). Preferably, Wequals the combined widths of several target locations on layer 16. Wcan have a substantially uniform value along the boundary 56 of layer 16or it can vary along boundary 56 as desired. Peripheral denser region 54serves for maintaining the accuracy per the required resolution. In thepreferred embodiment in which leveling is employed, region 54 servesalso for enhancing the sheerness of the edge of the layer after beingleveled.

FIGS. 7a-7d schematically illustrate a side view of the formed layerbefore (FIGS. 7a-7b ) and after (FIGS. 7c-7d ) leveling. FIGS. 7a and 7cillustrate a layer of uniform droplet density over the whole layer(either high droplet density with uniform dilution, or small dropletdensity without dilution). As shown in FIG. 7 c, after leveling, theboundary 56 is substantially round. FIGS. 7b and 7d illustrate a highdroplet density layer with dilution except at the periphery region 54.In which case, after leveling boundary 56 is much steeper than in FIG. 7c.

Local dilution can also be performed when it is desired to reduce theproduced waste. The waste ratio of a layer is defined as the amount ofexcess material 39 (see FIG. 2c ) which is discarded by leveling device32 during the leveling of the layer, expressed as a percentage orfraction of the total amount of material which is dispensed during theformation of the layer. The waste ratio induced by leveling device 32generally depends on the thickness of the layer and the desired buildquality. Specifically, the waste ratio is a decreasing function of thethickness and an increasing function of the build quality. The reasonfor the latter is that build quality (per a given build resolution)depends on the sharpness of the layer edge. Larger waste ratio meansthat the leveling apparatus discards more material, and as a consequencethe layer edge becomes sharper. Sufficiently high build quality can beachieved by controlling the amount of building material which isdiscarded by the leveling device. Broadly speaking, if the amount ofdiscarded material is too low, dripping of building material may befound on vertical walls of the object.

For example, it was found by the present Inventors that for a layerthickness of about 16 μm (after leveling), sufficiently high buildquality is achieved when the leveling device discards about 25% of thematerial, and for a layer thickness of about 32 μm (after leveling),sufficiently high build quality is achieved when the leveling devicediscards about 20% of the dispensed material.

In a conventional three-dimensional ink-jet printing apparatus, thewaste ratio ranges typically from about 10% for thick layers with lowbuild quality to about 30% for thin layers with high build quality. Itwas found by the inventor of the present invention that the waste ratiocan be reduced while maintaining the desired build quality. As stated,the objectives of leveling device 32 are, inter alia, to eliminateundesired patterns and sharpen the edges of the layers. Successfulaccomplishment of these objectives ensures the three-dimensionalformation of an object having substantially smooth surfaces and accurateoutlines. For these objectives to be accomplished, it is sufficient todispense a larger amount of material at exterior or near-exteriorregions of the layer, while diluting the spread of material in otherregions. Thus, in various exemplary embodiments of the invention thespread of building material in the layer is diluted so as to minimizethe amount of excess material 39 collected by the waste collectiondevice, while at the same time maintaining the predetermined resolutionand edge sharpness (and as a consequence—object's quality) at theexterior surfaces of the object.

This can be achieved by defining, for each layer, one or more interiorregions, and diluting the spread of material exclusively in the interiorregion(s) while maintaining the full (undiluted) amount of dispensedmaterial at any region other than the interior region(s).

The procedure can be better understood with reference to FIGS. 8a -8 b.FIG. 8a is a schematic illustration of a layer 70 in a plane parallel tothe X-Y plane, and FIG. 8b is a schematic illustration ofthree-dimensional object 12 as projected on a plane parallel to the X-Z.The Z level of layer 70 is illustrated in FIG. 8b as a horizontal lineparallel to the X axis.

Shown in FIG. 8 a, are four regions, designated by numerals 72, 74, 76and 78. Following the leveling of layer 70, each of regions 72, 76 and78 is expected to be in horizontal and/or vertical proximity to one ofthe exterior surfaces of the three-dimensional object 12. Thus, regions72, 76 and 78 are not interior regions of layer 70. More specifically,region 72 includes all the target locations which are expected to be inhorizontal proximity to the surrounding surface 73 of object 12, region76 includes all the target locations which are expected to be invertical proximity to the bottom surface 77 of object 12, and region 78includes all the target locations which are expected to be in verticalproximity to the top surface 79 of object 12.

Unlike regions 72, 76 and 78, region 74 is an interior region. That is,region 74 is characterized by a sufficiently large distance from theclosest exterior surface of the object. The interiority of region 74 canbe ensured by defining region 74 such that min(d₁, d₂, d₃)>d_(T), whered₁, d₂ and d₃ are, respectively, the minimal distances between region 74and the top 79, bottom 77 and surrounding 73 surfaces, and d_(T) is apredetermined threshold distance. A typical threshold distance is fromabout 0.5 mm to about 2 mm.

By diluting the spread of material exclusively in region 74 andmaintaining the predetermined resolution in other regions the wasteratio can be reduced by a factor of at least 2, or preferably 3, 4 or 5.

Reference is now made to FIG. 9 which is a flowchart diagram of apreferred method for preparing a bitmap corresponding to a predeterminedresolution of a layer, according to various exemplary embodiments of thepresent invention. The predetermined resolution can be characterized bya high density of columns. Typically, the resolution is above 600 dpi,and preferably above 720 dpi, for example, about 1200 dpi.

The method begins at step 80 and continues to step 81 in which apreliminary bitmap of the layer is prepared according to thepredetermined resolution in the X direction. For example, a 1200 dpioperating bitmap can be prepared. The method continues to step 82 inwhich expected layer thickness is calculated. The calculation of theexpected thickness is based on the obtained high resolution preliminaryoperating bitmap, the type of building material and the volume thereofin the occupied target locations. The method continues to step 83 inwhich the ratio between the calculated thickness and the desiredthickness is calculated. Denoting the thickness resulting from thehigh-resolution preliminary bitmap by h_(hr) and the desired thicknessby h₀, the ratio R is defined as h_(hr)/h₀. The ratio R is preferablylarger than unity because the high-resolution operating bitmap typicallyresults in greater thickness than required. A typical value for R is,without limitation, from about 1.2 to about 2.

The method continues to step 84 in which a dilution transformation isapplied to the preliminary bitmap. As explained above, the dilutiontransformation corresponds to dilution of building material spread inthe layer. The dilution transformation is applied based on thecalculated ratio, R. For example, R=1.5 can correspond to a 33%dilution. The dilution can be made in the X direction or, morepreferably, in both the X and Y directions.

The method ends at step 85.

The present embodiments successfully provide solutions for the case inwhich the density of rows exceeds its optimal value.

Printing layers with a higher Y resolution than density of nozzles inthe Y direction can be performed in more than one way. In one preferredembodiment, the head performs two or more X scans, while employing aninterlaced printing method. When the layer dimension in the Y directionis larger than the dimension of the head in the Y direction, more Xscans of the head can be performed to complete the layer. According to apreferred embodiment of the present invention the Y resolution is equalto the density of nozzles in the Y direction multiplied by a naturalnumber.

In interlaced printing, the head prints, for example, every second,third, etc. row, rather than every successive row. Once a scan iscompleted, the head performs a subsequent scan and prints the rows orpart of the rows that were skipped in the previous scans. The subsequentscans can be performed either at the same vertical level or at avertical level which is shifted with respect to the previous scan. Inthe case of two scans per layer, for example, the interlaced portionswhich are produced in each such scan are referred to as “odd-rows” and“even-rows”, respectively, corresponding to odd-number and even-numberlines of the bitmap. The interlacing is performed by shifting the headin the Y direction between successive X scans until the nozzles areproperly positioned for printing some or all the previously skippedrows.

As will be appreciated by one of ordinary skill in the art, when theresolution in Y direction is larger than the optimal row density and theoptimal density is larger or equal to the density of nozzles, more thanone scan is required for each layer. Moreover, in part of the scans, therows may land on the top of the rows of preceding scans of the samelayer, since the number of rows per unit Y length in the same plane islimited. According to a preferred embodiment of the present invention,for each such layer the leveling device (and optionally the printinghead) is at a first Z level during the first group of scans in which therows fill the first level (referred to herein as sub-layer), a second Zlevel during the second group of scans in which the rows fill the secondlevel, a third Z level in the third group of scans, etc. The nozzles ineach scan are preferably interlaced with the nozzles in the precedingscans so as to add rows between rows of the preceding scans. Thepreferred number of groups equals the Y resolution divided by theoptimal row density. Optionally, the rows in a scan group are added ontop of rows of the preceding scan groups.

In various exemplary embodiments of the invention each scan is performedso as to dispense substantially the same number of rows, and the heightdifferences between successive groups of scans (of the same layer) areuniform. Specifically, denoting the number of groups of scans per layerby n and the layer thickness by ΔZ, the Z level difference dZ betweensuccessive groups of scans preferably equals dZ=ΔZ/n.

For example, suppose that the density of the head's nozzles is 75 dpi,the optimal row density is 300 dpi, the required row resolution is 600dpi and layer thickness ΔZ is about 30μm. In this case n=600/300=2,dZ=30/2=15 and the head preferably scans 8 times over the object inorder to fabricate one original layer. Half of the scans may beperformed when the head moves in a forward (+X) direction and the otherhalf when the head moves in the reverse or backward (−X) direction. Ineach scan, all nozzles are operative and the rows are dispensed at adensity of 75 dpi, with a Y shift of the head between successive scansto ensure interlacing. Preferably the Y shift is selected so as to printeach row substantially in the center between two previously printedrows, thereby improving the fabrication quality of the layer. The first4 scans form a first sub-layer and are dispensed with the levelingdevice at a given height above the tray (until the optimal row densityis reached). The second 4 scans form a second sub-layer, and aredispensed with the roller at a height of about 15 μm above the formerheight.

The computation of the bitmap for performing the scans (8 scans perlayer, in the present example) can be performed in more than one way. Inone embodiment, the data for the required row resolution (600 dpi datain the present example) is computed once for all the scans as if thebuilding material comprises a single thick layer. In another embodiment,the data for the first sub-layer is computed in accordance with thefirst height of the roller (relative to the tray), while the data forthe second sub-layer is computed in accordance with the second height ofthe roller. For each sub-layer it is sufficient to compute the part ofthe bitmap, which corresponds to the rows printed in the respectivescans (4 scans in the present example). Alternatively, all rows thatcomprise the required row resolution for a given Z level are computedfor each sublayer, although only part of the computed rows (e.g., evenrows, odd rows) is actually dispensed.

When the rows of a high Y resolution layer are dispensed in two or moreinterlaced sub-layers, Y resolution of the resultant build is verysimilar to Y resolution of an object built in a single sub-layer using adenser nozzle array. This is particularly the case for thin sub-layers,because when the sub-layers are thin, the rows of the differentsub-layers can be viewed as printed substantially in the same plane (andthus preserving the high Y resolution). When the rows are also computedin the very Z level of the respective sub-layers, it will be appreciatedthat since the data relating to each sub-layer corresponds to the Zlevel of the sub-layer, a high Z resolution of 1/dZ (which is largerthan 1/ΔZ) is achieved.

The preparation of a bitmap for each sub-layer is favored from the standpoint of product quality (higher vertical resolution) and thepreparation of a bitmap once per layer is favored from the stand pointof manufacturing cost (reduced computer resources).

The different bitmaps of all layers and sub-layers are preferablyprepared and read with respect to the same horizontal reference frame ofthe virtual object or of the tray. Technically, it may be required toshift the Y origin of the sub-layers from one another with respect tothe virtual object, due to the lower Y resolution of the sub-layer ascompared to that of the present layer. In this case a respective shiftof the origin with respect to the tray (or to the object) is preferablyperformed while printing the sub-layers.

It is recognized that inaccuracies and/or imperfections which may occurin the final object, may have serious consequences. For example, whenthe object includes two or more parts designed to fit together, a slightinaccuracy may render the assembly of the parts impossible.Imperfections in the printed object may occur, for example, when one ormore nozzles of the printing head are wholly or partially blocked,defective or non-functional.

Reference is now made to FIG. 10 which is a schematic illustration ofnozzle array 17 in which there are three defective nozzles, designatedby numeral 92. Also illustrated in FIG. 10 is a top view of layer 16formed of occupied locations 96 printed by array 17, and bitmap 60defined with respect to a reference frame having an origin 95. Forbetter understanding of the relationship between layer 16 and bitmap 60,layer 16 overlays bitmap 60. The elements of bitmap 60 which are notoverlaid by layer 16 represent void locations 98. It is to be understoodthat in reality there is no overlaying relation between layer 16 andbitmap 60, because layer 16 is a physical object while bitmap 60 isvirtual. Nevertheless both occupied locations 96 and void locations 98correspond to physical locations on layer 16.

When the printing head includes one or more defective nozzles 92, thereis an insufficient amount of or no building material in target locationsvisited by the defective nozzles. Such target locations are referred toherein as “defective locations”, and are designated in FIG. 10 bynumeral 94. It is to be understood, however, that not all targetlocations which are not occupied by building material are defective. Oneof ordinary skill in the art would appreciate the difference betweendefective locations 94 and void locations 98, the latter being definedas target locations which are not designated to be occupied by buildingmaterial.

As illustrated in FIG. 10, the existence of defective nozzles 92 resultsin the formation of defective sectors 93 of missing or insufficientbuilding material.

The present embodiments successfully address the problem associated withdefective or non-functional nozzles in three-dimensional printing.According to a preferred embodiment of the present invention, controller18 ensures that array 17 dispenses an increased (e.g., double) amount ofbuilding material in occupied locations located just above defectivesectors 93. The procedure is further explained hereinunder withreference to FIG. 11.

FIG. 11 is a flowchart diagram of a method for three-dimensionalprinting of an object, according to various exemplary embodiments of thepresent invention, using a three-dimensional printing apparatus having aprinting tray and a printing head configured to dispense buildingmaterial through at least one nozzle array.

The method begins at step 100 and continues to step 101 in whichdefective nozzles and non-defective nozzles are detected. For example, anozzle test procedure may be executed periodically, in which theprinting head operates for one or more scans, in which test dropletseries are dispensed for each nozzle. The operator, or a nozzle detectorunit, may check the test printout to detect defective locations fromwhich the array-index of the defective nozzles can be inferred. Such aprintout may be done on tray 30, on a paper sheet attached to tray 30 oron another suitable medium. According to another technique, the nozzlearray jets series of droplets in nozzle-by-nozzle sequence onto a wastecontainer, with a droplet detector unit checking the emerging dropletsfrom each nozzle in order to determine the nozzle status. The dataindicating the status of nozzles may be stored in data processor 20 orcontroller 18 and later used by controller 18 as further detailedhereinbelow.

The method continues to step 102 in which the printing head is movedrepeatedly over the printing tray while dispensing the building materialto thereby form the layers. When the printing head includes defectivenozzles each formed layer inevitably includes defective sectors formedof the locations visited by the defective nozzles. The method continuesto step 103 in which an increased amount of building material isdispensed so as to compensate for the defective sectors in a precedinglayer by filling out the sector's dip.

Preferably, steps 102 and 103 are executed substantiallycontemporaneously. Thus, controller 18 ensures that, for each twoadjacent layers (say, layers i and i+1), non-defective sectors in theupper layer i+1 overlap defective sectors in the lower layer i, and thenozzles of said non-defective sectors dispense an increased amount ofbuilding material. In other words, layer i+1 is formed such that anincreased amount of building material is dispensed on the targetlocations which are substantially above defective sectors of layer i.

The overlap between non-defective sectors in the upper layer anddefective sectors in the lower layer can be achieved by shifting thehead in the Y direction between layers in a manner such thatnon-defective nozzles assume substantially the same Y coordinate as thedefective nozzles assumed in the preceding layer. Y shift ϕ that is usedfor compensating defective nozzles is typically measured in integerunits representing number of nozzles shifted. In addition to ϕ, Y isshifted one or more pixels in order to accomplish the Y interlacing, asrequired between different X scans. The overall shift ψ is an integernumber when measured in number of Y pixel steps. Each nozzle preferablyreceives printing information from the row of the bitmap whichcorresponds to the temporal Y position of the nozzle. It is expectedthat the compensating nozzles in the successive layer dispense twice thenormal amount of material so as to fully compensate for the previouslymissing material. Nevertheless, more layers may be required for fullcompensation. For example, when the amount of material is increased by afactor of 1.33, three layers are required for the compensation.

According to another embodiment of the present invention, thecompensation for missing material in a sector of a preceding layer isachieved without changing the dispensing rate of the nozzles. In thisembodiment, the compensation is achieved by the dispensed material in aset of k layers which immediately follow the defective sector. Thus foreach given layer, the controller preferably shifts the head in the Ydirection to ensure that non-defective nozzles scan rows which liesubstantially above the defective sector in k layers following the givenlayer. This procedure resembles the procedure of compensating formissing nozzles in U.S. Pat. No. 6,259,962, except that instead ofrandom shifts of Y from layer to layer, the shifts according to thepresent embodiments are selected from a predetermined series of shifts,based on the acquired information regarding the nozzles' status.

The algorithm which controls the shifting in the Y direction preferablyuses bitmap information of each individual layer, so as to ensure thatall or most of the defective sectors are treated. In addition, when aplurality of Y shifts series that accomplish the procedure are possible,the shifting algorithm can employ randomization so as to preventperiodical artifacts on the built object.

In the preferred embodiments in which leveling device 32 is employed(see FIGS. 2a and 2c ), the value of k is preferably selected accordingto the characteristic operation of device 32. This is because theoperation of device 32 may reduce the amount of building material nearthe defective region. For example, when device 32 trims a quarter of thelayer's thickness, the dip created by the defective nozzles is filled upafter 4 layers. In this case, the preferred value of k is at least 4.Still, as the number of possibilities to shift the head in Y direction(for a given full range of the horizontal shift ϕ) decreases with theincrease in the value of k, the minimal value of k (k=4 in the presentexample) is preferred. Typical value of the full range of ϕ is between10 and 150 nozzles. That means that ϕ can have integer values from 1 toa number between 10 and 150. The value of the full range of horizontalshift ϕ may be fixed in a machine (given in the machine designspecification), or may be modified according to the number of defectivenozzles and the size of defective clusters of nozzles. Modification ofthe full range of horizontal shift may be done manually by the user, orautomatically by the controller.

There is more than one way to ensure that the appropriate non-defectivesectors receive an increased (e.g., doubled) amount of buildingmaterial. In one embodiment, the driving voltage of the appropriatenon-defective nozzles is increased. In another, more preferredembodiment, the injection rate of the non-defective nozzles isincreased. This can be done, for example, by increasing the planardensity of the building material droplets (or pixels) dispensed bynozzles that move above defective sectors in a preceding layer.

FIG. 12 is a schematic illustration of a procedure for increasing theplanar density of the building material at the overlapping non-defectivesectors 110, according to a preferred embodiment of the presentinvention. Shown in FIG. 12, are nozzle array 17 with defective nozzles92, occupied locations 96 and the current bitmap 60. The printing headis shifted in Y direction by ψ w bitmap elements relative to itslocation in the previous layer. In the exemplified illustration of FIG.12, ψ=3. As there are 3 adjacent defective nozzles in head 17, the valueof ψ ensures that there is no overlap between the defective sector 93 ofthe current layer and the defective sectors of the previous layer. Thelatter are overlaid by a non-defective sector 110 of the current layer.

According to a preferred embodiment of the present invention bitmap 60is preferably prepared in accordance with the shape of the layer, butthe planar density of building material in sector 110 is larger than theplanar density in the other regions of the layer. In the presentexemplary embodiment, every other column in bitmap 60 has “1”s in thebitmap elements of the column (hence corresponds to occupied locations).

In contrast, all columns in sector 110 have “1”s in their bitmapelements. As will be appreciated by one ordinarily skilled in the art,such bitmap results in doubling the planar density of building materialin sector 110 relative to the other sectors. There is therefore anexcess of building material just above the defective sector of theprevious layer, which excess of building material percolates to theprevious layer and occupies its defective sectors.

When it is desired to dilute selective regions in the layer, e.g., forthe purpose of reducing waste and/or providing the layer with thedesired thickness and planar resolution, the dilution is preferablyperformed only in interior regions being scanned by non-defectivenozzles. More preferably, the dilution is performed only in regionswhich are interior regions and for which all target locations aresufficiently far from defective locations of the layer. Typically, thereis a distance of at least n target locations along the Y directionbetween each target location of a diluted region and the nearestdefective location of the layer. The parameter n can be any integerlarger than 1, e.g., 1<n<10. In addition, the dilution in the locations(or sectors) just above the defective locations (or sectors) in saidlayer is prevented in the m successive layers, where m is an integerlarger than 1, e.g., 1<m<10.

The advantage of the present embodiment is that it allows the handlingof defective nozzles by bitmap manipulation without altering the voltageof individual nozzles.

In the embodiment in which the increased amount of building material isprovided by increasing the driving voltage of the appropriatenon-defective nozzles, it is not necessary to employ bitmapmanipulation. In this embodiment, the controller preferably signals thehead to increase the volume of jetted droplets of the nozzles which scanrows above the defective sectors in a preceding layer, by increasedvoltage of the nozzle piezo-electric transducer. Typical volume increaseaccording to this technique is about ×1.2-1.3. Alternatively, thecontroller preferably signals the head to increase jetting frequency ofthe respective nozzles (without bitmap manipulation).

The compensation of defective sectors by increasing the dispensing ratecan be executed also for sub-layers. If, for example, five adjacentnozzles are defective or non-functional, each or selected X scans of thehead can be preceded by a Y shift selected such that the nozzles whichscan rows adjacent (in-between or near) to the defective rows of apreceding scan are non-defective, and are operated at increaseddispensing rate.

Another technique for handling defective nozzles which can be employedin various exemplary embodiments of the invention is the techniquedisclosed in U.S. Ser. No. 10/527,907, the contents of which are herebyincorporated by reference.

It is noted that the term “building material”, as used herein mayinclude model or “modeling” material, support material, mixed materialand/or any suitable combination of materials used in the building,forming, modeling, printing or other construction of three-dimensionalobjects or models. Building material may include material used to createobjects, material used to modify such material (e.g., dye, filler,binder, adhesive etc.), support material or other material used in thecreation of objects, whether or not appearing in the final object. Theterm “construction” as used herein may include different types and/orcombinations of building materials. For example, support constructionsmay include pillars built from modeling material surrounded by supportmaterial. A construction including a single, homogenous material mayalso be regarded as a construction according to embodiments of thepresent invention. The term “object” as used herein may include astructure that includes the object or model desired to be built. Such astructure may, for example, include modeling material alone or modelingmaterial with support material. The terms “support” or “supportconstruction” as used herein may include all structures that areconstructed outside the area of the object itself. The terms “layer” or“slice” as used herein may include portions of an object and/oraccompanying support structures optionally laid one above the other inthe vertical (e.g., Z) direction. The word layer may also be used todescribe a three-dimensional envelope or skin.

According to various exemplary embodiments of the present invention, thebuilding materials that may be used may be similar to the materialsdescribed in the aforementioned patent and patent applications (see,e.g., U.S. Pat. Nos. 6,259,962, 6,569,373, 6,658,314, 7,183,335,6,850,334, U.S. patent application Ser. Nos. 10/716,426, 10/724,399,10/725,995, 10/537,458, 11/433,513, 11/518,295 and PCT publication no.WO/2004/096527). For example, photopolymer materials curable by theapplication of electromagnetic radiation or other materials suitable forthree-dimensional object construction may be used. The photopolymermaterial may be of various types, including, for example, a photopolymermodeling material which may solidify to form a solid layer of materialupon curing, and a photopolymer support material which may solidify,wholly or partially, or not solidify upon curing, to provide a viscousmaterial, a soft gel-like or paste-like form and/or a semi-solid form,e.g., that may be easily removed subsequent to printing. The varioustypes of photopolymer material may be dispensed separately or in anygiven combination, according to the hardness and/or elasticity of theobject desired to be formed or any of its parts, or the supportconstructions required to provide object support during construction.Materials other than those described in the above patents andapplications may also be used.

In the embodiments in which the object is formed by thestereolithography technique, the building material is preferably acurable liquid, such as, but not limited to, an ultraviolet curableliquid, capable of absorbing the curing radiation, fast curing andadhering. The curable liquid is preferably non-toxic and of lowviscosity. Suitable curable liquid for the present embodiments include,without limitation, mixtures of acrylate compounds with epoxy resins. Aprocess for making ultraviolet curable material is described in U.S.Pat. Nos. 4,100,141 and 5,599,651. Other appropriate curable liquidswill occur to those ordinarily skilled in the art for variousapplications.

In the embodiments in which a combination of powder and binder materialsare used, the powder material can be a ceramic powder or a ceramic fiberand the binder material can be inorganic, organic or metallic bindermaterial. Alternatively, a metal powder can be used with a metallicbinder or a ceramic binder. Still alternatively, a plastic powder can beused with a solvent binder or a plastic binder, such as, but not limitedto, a low viscosity epoxy plastic material. Other appropriatecombinations of powder and binder materials will occur to thoseordinarily skilled in the art for various applications.

It is expected that during the life of this patent many relevantthree-dimensional printing techniques and associated building materialswill be developed and the scope of the terms “three-dimensionalprinting” and “building material” is intended to include all such newtechnologies a priori.

It is appreciated that certain features of the invention, which are, forclarity, described in the context of separate embodiments, may also beprovided in combination in a single embodiment. Conversely, variousfeatures of the invention, which are, for brevity, described in thecontext of a single embodiment, may also be provided separately or inany suitable subcombination.

Although the invention has been described in conjunction with specificembodiments thereof, it is evident that many alternatives, modificationsand variations will be apparent to those skilled in the art.Accordingly, it is intended to embrace all such alternatives,modifications and variations that fall within the spirit and broad scopeof the appended claims. All publications, patents and patentapplications mentioned in this specification are herein incorporated intheir entirety by reference into the specification, to the same extentas if each individual publication, patent or patent application wasspecifically and individually indicated to be incorporated herein byreference. In addition, citation or identification of any reference inthis application shall not be construed as an admission that suchreference is available as prior art to the present invention.

What is claimed is:
 1. A method of three-dimensional fabrication of anobject, comprising: forming a plurality of layers in a configuredpattern corresponding to the shape of the three-dimensional object, andrescaling at least one layer of said plurality of layers along at leastone direction so as to compensate for post-formation shrinkage of saidlayer along said at least one direction, wherein said rescaling isselected based on a formation time of a layer.
 2. The method of claim 1,wherein said rescaling comprises rescaling digital data representing theobject.
 3. The method of claim 1, wherein, for all layers, saidrescaling is according to the formation time of a predetermined layer.4. The method of claim 1, wherein said rescaling comprises rescalingduring said formation of said plurality of layers.
 5. The method ofclaim 1, wherein said rescaling comprises rescaling along two horizontaldirections.
 6. The method of claim 1, wherein said rescaling comprisesrescaling along at least one horizontal direction and along a verticaldirection.
 7. The method of claim 6, wherein a scaling factor of saidrescaling along said vertical direction is less than a scaling factor ofsaid rescaling along said at least one horizontal direction.
 8. Themethod of claim 1, wherein said rescaling is a monotonically decreasingfunction of a formation time of said layer.
 9. The method of claim 1,wherein said function is a linear decreasing function of a formationtime of said layer.
 10. The method of claim 1, wherein for at least onerescaled layer, a location of a center of mass of said layer after saidrescaling is the same as a location of a center of mass of said layerbefore said rescaling.
 11. The method of claim 1, wherein said formingis executed such that a formation time of all layers is the same.
 12. Asystem for three-dimensional fabrication of an object, comprising: athree-dimensional fabrication apparatus, configured for forming aplurality of layers in a configured pattern corresponding to the shapeof the three-dimensional object; said three-dimensional fabricationapparatus having a controller configured to ensure that at least onelayer of said plurality of layers is rescaled along at least onedirection so as to compensate for post-formation shrinkage of said layeralong said at least one direction, wherein said rescaling is selectedbased on a formation time of a layer.
 13. The system of claim 12,wherein said controller is configured to rescale digital datarepresenting the object.
 14. The system of claim 12, wherein saidcontroller is configured to rescale all layers according to theformation time of a predetermined layer.
 15. The system of claim 12,wherein said controller is configured to rescale during said formationof said plurality of layers.
 16. The system of claim 12, wherein saidcontroller is configured to rescale along two horizontal directions. 17.The system of claim 12, wherein said controller is configured to rescalealong at least one horizontal direction and along a vertical direction.18. The system of claim 17, wherein a scaling factor of said rescalingalong said vertical direction is less than a scaling factor of saidrescaling along said at least one horizontal direction.
 19. The systemof claim 12, wherein said controller is configured to rescale accordingto a monotonically decreasing function of a formation time of aid layer.20. The system of claim 12, wherein said function is a linear decreasingfunction of a formation time of said layer.
 21. The system of claim 12,wherein for at least one rescaled layer, a location of a center of massof said layer after said rescaling is the same as a location of a centerof mass of said layer before said rescaling.
 22. The system of claim 12,wherein said controller is configured to ensure that a formation time ofall layers is the same.